Physical Sciences and Mathematics Commons^™

A Basis Theorem For Perfect Sets, Marcia J. Groszek, Theodore A. Slaman

Dartmouth Scholarship

We show that if there is a nonconstructible real, then every perfect set has a nonconstructible element, answering a question of K. Prikry. This is a specific instance of a more general theorem giving a sufficient condition on a pair M ⊂ N of models of set theory implying that every perfect set in N has an element in N which is not in M.

The Dirichlet Problem And Its Physical Motivations, Andrew E. Pitts

Honors Theses

In this work, we explore the basics of harmonic function theory and its relationship to problems in the theory of heat diffusion. In particular, we will focus on the classical Dirichlet problem.

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Robert Davis: In Memoriam, Carolyn A. Maher, Robert Speiser

Humanistic Mathematics Network Journal

No abstract provided.

Math Poem, Beth Corridori

Humanistic Mathematics Network Journal

No abstract provided.

The Poem Of Math, Michelle Wang

Humanistic Mathematics Network Journal

No abstract provided.

Randal Bishop Plunges Into 4-D Space: A Comment On Randal Bishop’S Paper Titled “The Use Of Realistic Imagery To Represent The Relationships In A Four-Dimensional Coordinate System”, Carlos Ernesto S. Lindgren

Humanistic Mathematics Network Journal

No abstract provided.

Thinking About The Preparation Of Teachers Of Elementary School Mathematics, Jane Wenstrom, Kathleen Martin, Susan King

Humanistic Mathematics Network Journal

No abstract provided.

Geometry In Nature, Rachel Finkelstein

Humanistic Mathematics Network Journal

No abstract provided.

Triangle, Ian Ross

Humanistic Mathematics Network Journal

No abstract provided.

Real Data, Real Math, All Classes, No Kidding, Martin Vern Bonsangue

Humanistic Mathematics Network Journal

No abstract provided.

The Use Of Realistic Imagery To Represent The Relationships In A Four-Dimensional Coordinate System, Randal J. Bishop

Humanistic Mathematics Network Journal

No abstract provided.

Problems That Matter: Teaching Mathematics As Critical Engagement, Jeffrey Bohl

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: The Courage To Teach By Parker Palmer, Sandra Z. Keith

Humanistic Mathematics Network Journal

No abstract provided.

On Solving Equations, Negative Numbers, And Other Absurdities: Part I, Ralph A. Raimi

Humanistic Mathematics Network Journal

No abstract provided.

The Poetics Of E=Mc2, Richard A. Schwartz

Humanistic Mathematics Network Journal

No abstract provided.

I Love To Add, Kyle Cotler

Humanistic Mathematics Network Journal

No abstract provided.

Death, Trial And Life, Prem N. Bajaj

Humanistic Mathematics Network Journal

No abstract provided.

Math Rules, Blake Mayer

Humanistic Mathematics Network Journal

No abstract provided.

Tessellations, Zan Jabara

Humanistic Mathematics Network Journal

No abstract provided.

The Smarandache Semantic Paradox, Anthony Begay

Humanistic Mathematics Network Journal

No abstract provided.

Mr. Trapezoid's Walk, Michael Pillar

Humanistic Mathematics Network Journal

No abstract provided.

Geometric Shapes, Sam Dudley

Humanistic Mathematics Network Journal

No abstract provided.

Fun With Algebra!, Janelle Kulik

Humanistic Mathematics Network Journal

No abstract provided.

Poem, Natalie Kashhefi

Humanistic Mathematics Network Journal

No abstract provided.

On Different Integrable Systems Sharing The Same Nondynamical R-Matrix, Zhijun Qiao, Walter Strampp

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In a recent paper @Zhijun Qiao and Ruguang Zhou, Phys. Lett. A 235, 35 ~1997!#, the amazing fact was reported that a discrete and a continuous integrable system share the same r-matrix with the interesting property of being nondynamical. Now, we present three further pairs of different continuous integrable systems sharing the same r-matrix again being nondynamical. The first pair is the finite-dimensional constrained system ~FDCS! of the famous AKNS hierarchy and the Dirac hierarchy; the second pair is the FDCS of the well-known geodesic flows on the ellipsoid and the Heisenberg spin chain hierarchy; and the third pair is …

A Comparison Of Deterministic And Stochastic Population Models, Clarissa Smith

Masters Theses & Specialist Projects

In this thesis, the author considers the exponential and the predator-prey population models. A comparison of the deterministic and stochastic versions of each is made. The author shows that on average a stochastic model is precisely its corresponding deterministic model. The first model considered is the exponential model. A solution is provided for both the deterministic and the stochastic versions. A predator-prey model is also analyzed. A solution of the stochastic predator-prey model is shown to be intractable. Analysis of this model is performed through numerical simulation.

Statistical Characterization Of Fluvial-Deltaic Reservoirs With Archetypes, Laura L. Watkins

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Optimizing the extraction of oil and other hydrocarbon products from existing sites is important. One source of hydrocarbon products is reservoirs found within sedimentary rock formations. Understanding fluid behavior within such formations can be quite useful in optimizing oil production. Fluid behavior within sedimentary formations is influenced by the bedform structure and permeabilities within the formation. Thus, we are concerned with developing a physically and statistically valid method of characterizing sedimentary rock formations. The use of archetypal analysis to generate synthetic bedforms, as well as the use of Kriging to assign permeabilities within a bedform, was explored. With these tools, …

Problems In Harmonic Function Theory, Ronald A. Walker

Honors Theses

Harmonic Function Theory is a field of differential mathematics that has both many theoretical constructs and physical connections, as well as its store of classical problems.

One such problem is the Dirichlet Problem. While the proof of the existence of a solution is well-founded on basic theory, and general methods for polynomial solutions have been well studied, much ground is still yet to be overturned. In this paper we focus on the examination, properties and computation methods and limitations, of solutions for rational boundary functions.

Another area that we shall study is the properties and generalizations of the zero sets …

Classification Of Hereditary Matrices, Jim Agler, J. W. Helton, Mark Stankus

Mathematics

A classical approach used to obtain basic facts in the theory of square matrices involves an analysis of the relationship between polynomials p in one variable and square matrices T such that p(T) = 0. We consider matrices and operators which satisfy a different type of polynomial constraint. Let H be a complex Hilbert space, T be a bounded linear transformation of H, T* be the adjoint of T, and C[x, y] be the algebra of polynomials in x and y with complex coefficients. For a polynomial p E C[x, y] in …